From the coefficient of correlation, the extent to which the readings of both in- 

 struments expressed in standard deviations measure ocean variability can be ob- 

 tained. This is derived as follows : 



Sx = ^x d-^')' (4) 



Where Ss- = standard error of estimate of y 

 S^ = standard error of estimate of x 



If the correlation is extremely high, the standard error of estimate corresponds 

 to the random errors of the instrument : 



From Section 4.3: 



"^y ^^T.' INSTR. (5) 



Thus: 



(7) 



Oy V (Ot^OCEAN "*" (-^TMNSTR. 



Combining Equations (3), (5) and (7) 



. 2 



[ 



'z 



(gT)lNSTR. = (n.r_„. + fn„)! 



l-r 



^^T'OCEAN "*" ^''T'' INSTR. (8) 



Which reduces to 



^^T^ OCEAN _ ^ 



^°T''lNSTR. V X-l 



The coefficient of correlation does not indicate the relative reliability of the in- 

 struments (Bathythermograph and bucket or injection thermometer) . The magni- 

 tude of the standard deviations must also be considered. 



When the coefficient of correlation is high and the standard deviations are 

 equal, the resulting standard errors of estimate are low, and both instruments 

 are relaible to the accuracy of the standard error of estimate. The ocean varia- 

 bility can then be measured by the standard deviations. 



When the coefficient of correlation is low and the standard deviations are also 

 low, there may be negligible ocean variability, assuming the conditions of 9.1.2 are 

 observed. 



When the coefficient of correlation is low, and the standard deviations are high, 

 one or both of the instruments has a high random error. If the magnitudes of the 

 two standard deviations are dissimilar, probably the instrument with the higher 

 standard deviation is the culprit. In any case, no reliability can be placed on the data 

 representing ocean variability. 



28 



